The Pokemon League music doesn't have a real name, it's just 'Pokemon League (Day)' and 'Pokemon League (Night)'.
I have to agree though, beautiful music.
Pokemon League (Day):
Pokemon League (Night):
The above links aren't that very long, only about 2 minutes, but some awesome YouTuber made an extended 15 minute version. It's Pokemon League (Day).
They are also on the Pokemon Diamond & Pokemon Pearl: Super Music Collection. The day version is Number 75 on Disk 1, the night version is Number 61 on Disk 2. On the iTunes release it's the same for the day version, and it's Number 139 for the night. Click here for it's iTunes listing.
Hope I helped. :)